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In summary: So given an electron with a given energy/momentum and a photon with a given energy/momentum then after absorption there would be two unknowns, the electron energy and momentum. However there are three equations:...After absorption, there are three unknowns: the electron energy, momentum, and the photon's energy and momentum. However, there are two equations: the conservation of energy and momentum. After absorption, there are three unknowns: the electron energy, momentum, and the photon's energy and momentum. However, there are two equations: the conservation of energy and momentum.

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Your proposed process cannot occur. It would violate energy or momentum conservation.

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Then, what would happen?Orodruin said:Your proposed process cannot occur. It would violate energy or momentum conservation.

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What would happen when? You have described an impossible process.e2m2a said:Then, what would happen?

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In the Compton effect, a photon scatters off of an electron. It is not absorbed. Both energy and momentum are conserved.

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This is not possible. You could have an atom absorb a photon, but not an electron. There is no way to conserve energy and momentum for the electron since it has no internal degrees of freedom.e2m2a said:Suppose it collides with an electron at rest and is completely absorbed by the electron

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Momentum and energy are always conserved no matter what.GreatestPhysician99 said:

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Yes. This is precisely why an isolated electron cannot absorb a photon. An isolated electron cannot absorb a photon while conserving energy and momentum. Therefore the process is forbidden.GreatestPhysician99 said:Momentum and energy are always conserved no matter what.

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Hmm why is it forbidden ? The photon's momentum and energy will be converted to electron's momentum and energy since the electron absorbes the photon.If it emmits it , the electron will lose momentum and energy...Dale said:Yes. This is precisely why an isolated electron cannot absorb a photon. An isolated electron cannot absorb a photon while conserving energy and momentum. Therefore the process is forbidden.

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Having no internal structure, the only energy the electron can possesses is kinetic. If we adopt a frame of reference in which the electron winds up at rest, we have an electron arriving with non-zero kinetic energy and combining with a photon that has non-zero kinetic energy. The result is an electron at rest. This obviously violates conservation of energy.GreatestPhysician99 said:Hmm why is it forbidden ? The photon's momentum and energy will be converted to electron's momentum and energy since the electron absorbes the photon.If it emmits it , the electron will lose momentum and energy...

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The electron will gain momentum (start moving ) according to the static frame of reference . So this is wrong.jbriggs444 said:Having no internal structure, the only energy the electron can possesses is kinetic. If we adopt a frame of reference in which the electron winds up at rest, we have an electron arriving with non-zero kinetic energy and combining with a photon that has non-zero kinetic energy. The result is an electron at rest. This obviously violates conservation of energy.

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There is no such thing as a "static frame of reference". All inertial frames of reference are equally valid, including the one in which the electron winds up at rest. Energy is required to be conserved in all of them. Momentum is required to be conserved in all of them.GreatestPhysician99 said:The electron will gain momentum (start moving ) according to the static frame of reference . So this is wrong.

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Again, this is simply incorrect.GreatestPhysician99 said:

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It can be conserved as relativistic momentum or energy.jbriggs444 said:There is no such thing as a "static frame of reference". All inertial frames of reference are equally valid, including the one in which the electron winds up at rest. Energy is required to be conserved in all of them. Momentum is required to be conserved in all of them.

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The math doesn’t work out. Remember that energy, mass, and momentum are related by ##m^2 c^2=E^2/c^2-p^2##. The mass of a photon is 0 and the mass of an electron is 511 keV/c.GreatestPhysician99 said:The photon's momentum and energy will be converted to electron's momentum and energy since the electron absorbes the photon.

So given an electron with a given energy/momentum and a photon with a given energy/momentum then after absorption there would be two unknowns, the electron energy and momentum. However there are three equations: the equation above, conservation of energy, and conservation of momentum. There is no solution to this set of three equations in two unknowns. Therefore absorption is forbidden.

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If the photon is absorbed by the electron we are left with a single particle with velocity zero and mass ##m_e\gamma (c+v)/c##. This does not describe an electron. Therefore an electron cannot absorb a photon.

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If one is anyway using 4-vectors, there is also a point in doing it without any reference to a frame. Calling the 4-momenta of the initial electron, final electron, and photon ##p_i##, ##p_f##, and ##k##, respectively, 4-momentum conservation reads ##p_i + k = p_f##. Squaring this we obtain (in units where ##c = 1##)Ibix said:

If the photon is absorbed by the electron we are left with a single particle with velocity zero and mass ##m_e\gamma (c+v)/c##. This does not describe an electron. Therefore an electron cannot absorb a photon.

$$

p_f^2 = m_e^2 = (p_i+k)^2 = p_i^2 + k^2 + 2p_i\cdot k = m_e^2 + 0 + 2p_i \cdot k > m_e^2,

$$

since ##p_i \cdot k > 0## due to the electron 4-momentum being time-like and being a non-zero null vector. Thus, we reach the false inequality ##m_e^2 > m_e^2## (note that the inequality is strict), which means the proposed process cannot satisfy 4-momentum conservation.

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